2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1e2c1dc4-3724-4bba-961c-1c2ae7e649c4-3_1463_1194_239_440}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A teacher buys pens and pencils. The number of pens, \(x\), and the number of pencils, \(y\), that he buys can be represented by a linear programming problem as shown in Figure 2, which models the following constraints:
$$\begin{aligned}
8 x + 3 y & \leqslant 480
8 x + 7 y & \geqslant 560
y & \geqslant 4 x
x , y & \geqslant 0
\end{aligned}$$
The total cost, in pence, of buying the pens and pencils is given by
$$C = 12 x + 15 y$$
Determine the number of pens and the number of pencils which should be bought in order to minimise the total cost. You should make your method and working clear.